Vector `veca` is prepedicular to `vecb`, componets of `veca- vecb` along `veca + vecb` will be :

Options

A. zero
B. a-b
C. `(a^(2)- b^(2))/(sqrt(a^(2)+ b^(2)))`
D. `sqrt(a^(2)+ b^(2))`

Answer

C

Explanation

`|veca- vecb|= cos theta`
`|veca- vecb|= |veca|^(2)+ |vecb|^(2)-0`
`= a^(2) + b^(2)`
`|veca- vecb|= sqrt(a^(2)+b^(2))`
`cos theta =((veca - vecb)(veca + vecb))/(|veca -vecb||veca + vecb|)=(a^(2)-b^(2))/((a^(2) +b^(2)))`
`|veca - vecb| cos theta = sqrt(a^(2) + b^(2))xx (a^(2)- b^(2))/(a^(2) +b^(2))`
`" "(a^(2)-b^(2))/(sqrt(a^(2) + b^(2)))`